The model predictive control is a control method for determining inputs to a control target at each step by optimizing responses up to a definite future time. This method is noteworthy as a control technique that enables the follow-up control to a non-stationary target value, and has a merit that constraint conditions such as saturation can be treated.
Conventionally, the study was mainly made for the linear system, however, recently, the study is actively made for the application to the non-linear system. At present, there are a lot of application examples that the non-linear problem is simplified to the linear problem. However, it is not easy to actually apply this technique to a case that high-speed changes occur even in the linear system, and it is desired that the calculation period is shortened.
Methods for processing a problem for the model predictive control in real time, which also includes a control target having a non-linear plant model are largely classified to two categories. One is a method that the state feedback control rule is represented by a function of a state x(k) of the plant off-line, and only substitution calculation is carried out online. On the other hand, the other method is a method that all calculation is carried out online.
As for the calculation carried out off-line, a method is considered that spaces of the present states x(k) of the plant are classified by a certain method such as return to Hamilton-Jacobi-Bellman method, and feedback control rules are given to the respective space regions. However, according to such a method, too many space regions may be generated. Moreover, if the number of dimensions of the states increases, the number of divisions rapidly increases.
On the other hand, as for the method for carrying out the calculation online, various numerical analysis method of optimization problems, such as gradient method, interior point method or the like, can be applied. In addition, a method for efficiently solving the problem by gasping the dual problem with respect to Lagrange multiplier and an algorithm that a structure such as Hessian matrix is used to improve the efficiency are advocated. However, when the normal iterative calculation is used as a method of the numerical calculation, the calculation is iterated until the solution is settled. Therefore, the calculation amount becomes huge.
Then, a method is considered to reduce the iteration calculations by the continuous deformation analysis using the time as a parameter. Even in such a case, when the change of the states x(k) of the plant is large, the number of iterations becomes large. Therefore, any step may not be completed within a desired period.
In addition, as for the numerical analysis method, a lot of approximations are used for the expression in the optimization problem in order to efficiently obtain the solution. Therefore, a large gap with the value to be intrinsically obtained may occur.
Namely, there is no technique for calculating the inputs for the plant at high speed in the model predictive control.